Biology related question. How would you get rid of the mice based on information given?

Consider the following scenario. You suddenly realize that you have a population of mice living in your attic. You do not want to put out traps or poison, so you decide to get a cat. The cat is fast; however, the cat is not as fast as the very fast mice. There are a total of 20 mice living in the attic. Of the 20 mice, 10 are very fast, 5 are medium fast, and 5 are very slow